Question: Simplify the following expression: $p = \dfrac{20t^3 - 8t^2}{24t^2}$ You can assume $t \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $20t^3 - 8t^2 = (2\cdot2\cdot5 \cdot t \cdot t \cdot t) - (2\cdot2\cdot2 \cdot t \cdot t)$ The denominator can be factored: $24t^2 = (2\cdot2\cdot2\cdot3 \cdot t \cdot t)$ The greatest common factor of all the terms is $4t^2$ Factoring out $4t^2$ gives us: $p = \dfrac{(4t^2)(5t - 2)}{(4t^2)(6)}$ Dividing both the numerator and denominator by $4t^2$ gives: $p = \dfrac{5t - 2}{6}$